A certain colony of bacteria

Question

A certain colony of bacteria is growing at 4% daily. If the culture of bacteria has a population of 4,000 today, what will it be after 10 days?

Answer 1

Say you have population of $P_0$ on day $0$: day-$0$: $P_0$

and on day-$1$ you have day-$1$: $P_1 = P_0 + 0.04 P_0 = 1.04\times P_0$

day-$2$: $P_2 = P_1 + 0.04 P_1 = 1.04 P_1 =1.04(1.04P_0) = 1.04^2 P_0$

day-$3$: $ P_3 = P_2 + 0.04 P_2 = 1.04 P_2 = 1.04(1.04^2P_0) = 1.04^3 P_0$

so on day $n$ you have

$ P_n = P_{n-1} + 0.04 P_{n-1} = 1.04 P_{n_1} =1.04(1.04^{n-1}P_0) = 1.04^n P_0$

Set $n=10$ and $P_0=4000$ and you have answer!